lu.cpp

强大的C++库

/*!
 * \file
 * \brief Implementation of LU factorisation functions.
 * \author Tony Ottosson
 *
 * -------------------------------------------------------------------------
 *
 * IT++ - C++ library of mathematical, signal processing, speech processing,
 *        and communications classes and functions
 *
 * Copyright (C) 1995-2008  (see AUTHORS file for a list of contributors)
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
 *
 * -------------------------------------------------------------------------
 */

#ifndef _MSC_VER
#  include <itpp/config.h>
#else
#  include <itpp/config_msvc.h>
#endif

#if defined(HAVE_LAPACK)
#  include <itpp/base/algebra/lapack.h>
#endif

#include <itpp/base/algebra/lu.h>
#include <itpp/base/specmat.h>


namespace itpp {

#if defined(HAVE_LAPACK)

  bool lu(const mat &X, mat &L, mat &U, ivec &p)
  {
    it_assert_debug(X.rows() == X.cols(), "lu: matrix is not quadratic");
    //int m, n, lda, info;
    //m = n = lda = X.rows();
    int m = X.rows(), info;

    mat A(X);
    L.set_size(m, m, false);
    U.set_size(m, m, false);
    p.set_size(m, false);

    dgetrf_(&m, &m, A._data(), &m, p._data(), &info);

    for (int i=0; i<m; i++) {
      for (int j=i; j<m; j++) {
	if (i == j) { // diagonal
	  L(i,j) = 1;
	  U(i,j) = A(i,j);
	} else { // upper and lower triangular parts
	  L(i,j) = U(j,i) = 0;
	  L(j,i) = A(j,i);
	  U(i,j) = A(i,j);
	}
      }
    }

    p = p - 1; // Fortran counts from 1

    return (info==0);
  }

  // Slower than not using LAPACK when matrix size smaller than approx 20.
  bool lu(const cmat &X, cmat &L, cmat &U, ivec &p)
  {
    it_assert_debug(X.rows() == X.cols(), "lu: matrix is not quadratic");
    //int m, n, lda, info;
    //m = n = lda = X.rows();
    int m = X.rows(), info;

    cmat A(X);
    L.set_size(m, m, false);
    U.set_size(m, m, false);
    p.set_size(m, false);

    zgetrf_(&m, &m, A._data(), &m, p._data(), &info);

    for (int i=0; i<m; i++) {
      for (int j=i; j<m; j++) {
	if (i == j) { // diagonal
	  L(i,j) = 1;
	  U(i,j) = A(i,j);
	} else { // upper and lower triangular parts
	  L(i,j) = U(j,i) = 0;
	  L(j,i) = A(j,i);
	  U(i,j) = A(i,j);
	}
      }
    }

    p = p - 1; // Fortran counts from 1

    return (info==0);
  }

#else

  bool lu(const mat &X, mat &L, mat &U, ivec &p)
  {
    it_error("LAPACK library is needed to use lu() function");
    return false;
  }

  bool lu(const cmat &X, cmat &L, cmat &U, ivec &p)
  {
    it_error("LAPACK library is needed to use lu() function");
    return false;
  }

#endif // HAVE_LAPACK


  void interchange_permutations(vec &b, const ivec &p)
  {
    it_assert(b.size() == p.size(),"interchange_permutations(): dimension mismatch");
    double temp;

    for (int k=0; k<b.size(); k++) {
      temp=b(k);
      b(k)=b(p(k));
      b(p(k))=temp;
    }
  }

  bmat permutation_matrix(const ivec &p)
  {
    it_assert (p.size() > 0, "permutation_matrix(): vector must have nonzero size");
    int n = p.size(), k;
    bmat P, identity;
    bvec row_k, row_pk;
    identity=eye_b(n);


    for (k=n-1; k>=0; k--) {
      // swap rows k and p(k) in identity
      row_k=identity.get_row(k);
      row_pk=identity.get_row(p(k));
      identity.set_row(k, row_pk);
      identity.set_row(p(k), row_k);

      if (k == n-1) {
	P=identity;
      } else {
	P*=identity;
      }

      // swap back
      identity.set_row(k, row_k);
      identity.set_row(p(k), row_pk);
    }
    return P;
  }

} // namespace itpp